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http://elar.urfu.ru/handle/10995/101571
Название: | Interpolating wavelets on the sphere |
Авторы: | Chernykh, N. I. |
Дата публикации: | 2019 |
Издатель: | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences |
Библиографическое описание: | Chernykh N. I. Interpolating wavelets on the sphere / N. I. Chernykh. — DOI 10.15826/umj.2019.2.001 // Ural Mathematical Journal. — 2019. — Vol. 5. — Iss. 2. — P. 3-12. |
Аннотация: | There are several works where bases of wavelets on the sphere (mainly orthogonal and wavelet-like bases) were constructed. In all such constructions, the authors seek to preserve the most important properties of classical wavelets including constructions on the basis of the lifting-scheme. In the present paper, we propose one more construction of wavelets on the sphere. Although two of three systems of wavelets constructed in this paper are orthogonal, we are more interested in their interpolation properties. Our main idea consists in a special double expansion of the unit sphere in R3 such that any continuous function on this sphere defined in spherical coordinates is easily mapped into a 2π-periodic function on the plane. After that everything becomes simple, since the classical scheme of the tensor product of one-dimensional bases of functional spaces works to construct bases of spaces of functions of several variables. © 2019, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences. All rights reserved. |
Ключевые слова: | BEST APPROXIMATION INTERPOLATING WAVELETS MULTIRESOLUTION ANALYSIS SCALING FUNCTIONS TRIGONOMETRIC POLYNOMIALS WAVELETS |
URI: | http://elar.urfu.ru/handle/10995/101571 |
Условия доступа: | info:eu-repo/semantics/openAccess |
Идентификатор РИНЦ: | 41672789 |
Идентификатор SCOPUS: | 85078782898 |
Идентификатор PURE: | 12012044 a4469820-bf5f-4243-aac5-5301f122dcf9 |
ISSN: | 24143952 |
DOI: | 10.15826/umj.2019.2.001 |
Располагается в коллекциях: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
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Файл | Описание | Размер | Формат | |
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2-s2.0-85078782898.pdf | 169,34 kB | Adobe PDF | Просмотреть/Открыть |
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